March Madness: The Math Behind Marcus Paige and Kris Jenkins' Last-Second Three-Pointers

Kris Jenkins put the exclamation point on Villanova's historic run through the NCAA Tournament. How unlikely was it?

With one shot Monday night, Villanova's Kris Jenkins claimed his place in NCAA Tournament history with his buzzer-beating three-pointer, as Villanova knocked off North Carolina 77-74 to claim their second National Championship in school history.

But before we get to the clips of the confetti falling from the ceiling, we have to take a look at what made the game special before Jenkins tossed the ball in bounds to Ryan Arcidiacono with 4.7 seconds left and the game tied at 74.

At the start of the game, North Carolina had a win probability of 57 percent, according to  numberFire Live. A back-and-forth first half gave both teams a favorable win probability at some point in the first 20 minutes. However, with UNC leading 39-34 at the half, their win probability rose to 76 percent.

North Carolina extended their lead to seven in the opening moments of the second half, which would be their largest lead of the game. The Wildcats clawed their way back into the game, finally taking the lead back with 13:26 to go, when Phil Booth's two-pointer put Nova up 46-44, raising their win probability up to 52 percent. For the next eight and a half minutes, Villanova slowly increased their lead, peaking at 67-57 inside of six minutes. The Wildcats' win probability was 94 percent, as they looked to milk away the clock and claim the title.

The Tar Heels did not go down without a fight, chipping away at Villanova's lead, getting as close as a single point two different times in the final minute of the game. After two Josh Hart free throws grew the Wildcats' lead to 74-71 with 13 seconds remaining, UNC's win probability dwindled to just seven percent.

Grasping for one more breath, North Carolina's season rested in the hands of Marcus Paige, after his defender, Daniel Ochefu, dove to the floor attempting a steal, leaving Paige open on the wing. A closeout by Ryan Arcidiacono forced Paige to double-clutch, but he nailed the three anyway, tying the game at 74 and increasing UNC's win probability by 35 percentage points, up to 42 percent.

Finally, with 4.7 seconds left, Jenkins in bounded to Arcidiacono, who ran up the left side of the court. Jenkins charged down the floor and met back up with Arcidiacono to receive the short shovel pass and step into his shot. 

Because it was the final play of the game, Villanova's win probability went up 41 percentage points and sealed the victory, leading to this gem of a win probability graph.

Whether it was clutch, luck, or a little of both, the three-pointers by Marcus Paige and Kris Jenkins in the final 13.5 seconds of the 2016 Men's National Championship will go down as one of the greatest sequences in the history of the tournament.

Jenkins' big shot is the first buzzer-beater in a National Title game since Lorenzo Charles' put-back dunk in 1983 lifted North Carolina State over Houston.